Did Kirchoff law fail?
Electricity and Magnetism
Level
3
What is the current in the 40 ohm circuit, and hence find the total power delivered by the two voltage sources.
This problem is original.
4.4 A, 44 watts
4 A, 40 watts
0 A, 0 watts
The circuit violates Kirchoff voltage law. Circuit not possible.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Taking I1 and I2 to be the branch currents in the LHS and the RHS circuits respectively, Kirchhoff's Voltage Law (KVL) requires:
(I1 - I2) 40 = 10 (LHS branch); (I2 - I1) 40 = 10 (RHS branch).
assuming clockwise is positive-signed. However, this 2x2 linear system is inconsistent as we obtain:
I1 - I2 = 1/4 & I1 - I2 = -1/4.
Also, solving the system via Cramer's Rule reveals both I1 & I2 tend to infinity!
Thus, no such circuit can be achieved since it violates KVL.